Relation between Change in Potential Energy and Work Done

Why is dU=-$\vec{F}$.d$\vec{r}$
Integrating with putting the limits on we get:
ΔU=-W
Why is this? Here $\vec{F}$ is a conservative force/Force field.

hi andyrk!

potential energy is simply another name for (minus) the work done by a conservative force

Does it have any proof? Or is it just stated out of nowhere?

Potential Energy is actually defined that way. It doesn't require a proof.

tiny-tim